Mopping systems incorporating replaceable sponge-based refills are generally known. By way of example, replaceable sponge-based mop heads are described in U.S. Pat. Nos. 4,216,562 to Strahs, 6,058,552 to Hanan and 6,148,465 to Hsieh et al., the teaching of all of which are incorporated herein by reference. As will be appreciated, prior mop constructions have typically relied on relatively complex clamping systems, solid surface attachment plates, and/or threaded attachment elements such as screws and the like in order to provide a desired operative connection between a replaceable refill and the handle structure. Each of these attachment systems has certain inherent limitations. By way of example, systems which utilize clamping engagement between a mop head and handle structure may require a relatively complex clamp structure which may tend to corrode or otherwise degrade over time in the presence of cleaning solutions. Likewise, mop systems which utilize screws and/or other threaded fasteners may be prone to premature failure at the point of mechanical connection. Systems which utilize foam refills backed by solid surface connection plates may rely on relatively complex attachment mechanisms for connection to mop frames.